Increases in the low attenuation areas (LAA) of chest x-ray computed tomography images in patients with chronic obstructive pulmonary disease (COPD) have been reported to ref lect the development of pathological emphysema. We examined the statistical properties of LAA clusters in COPD patients and in healthy subjects. In COPD patients, the percentage of the lung field occupied by LAAs (LAA%) ranged from 2.6 to 67.6. In contrast, LAA% was always <30% in healthy subjects. The cumulative size distribution of the LAA clusters followed a power law characterized by an exponent D. We show that D is a measure of the complexity of the terminal airspace geometry. The COPD patients with normal LAA% had significantly smaller D values than the healthy subjects, and the D values did not correlate with pulmonary function tests except for the diffusing capacity of the lung. We interpret these results by using a large elastic spring network model and find that the neighboring smaller LAA clusters tend to coalesce and form larger clusters as the weak elastic fibers separating them break under tension. This process leaves LAA% unchanged whereas it decreases the number of small clusters and increases the number of large clusters, which results in a reduction in D similar to that observed in early emphysema patients. These findings suggest that D is a sensitive and powerful parameter for the detection of the terminal airspace enlargement that occurs in early emphysema.High-resolution computed tomography (CT) is a sensitive and noninvasive tool for assessing alterations in lung structure induced by various disease processes. Increases in the low attenuation areas (LAA) in the lung regions of chest x-ray CT images in patients with chronic obstructive pulmonary disease (COPD) have been reported to reflect the development of pathological emphysema (1-4). Nevertheless, previous methods of analyzing lung CT images are limited for general clinical diagnostic purposes (5) because the size and spatial distribution of LAAs are not taken into account. Recently, Uppaluri et al. (6) found that a texture-based adaptive multiple feature method could differentiate between normal and emphysematous tissue with 100% accuracy. However, it is not clear whether this method would detect early emphysema. More recently, Shimizu et al. (7) proposed a promising fractal analysis method for assessing ground-glass opacities in lung CT images. Their approach was able to successfully differentiate between fibrotic and nonfibrotic disease processes.The concept of fractal geometry was developed by Mandelbrot (8) to quantitatively describe the random variations in size and shape seen in natural objects. A fractal object is said to be scale-free because its characteristics are invariant under isotropic scale transformations. Such scale-invariance can be achieved if the object is formed by parts that are similar to the whole. In other words, fractals are self-similar and hence are characterized by power law functions (the only mathematical functions obeying s...

Collagen and elastin are thought to dominate the elasticity of the connective tissue including lung parenchyma. The glycosaminoglycans on the proteoglycans may also play a role because osmolarity of interstitial fluid can alter the repulsive forces on the negatively charged glycosaminoglycans, allowing them to collapse or inflate, which can affect the stretching and folding pattern of the fibers. Hence, we hypothesized that the elasticity of lung tissue arises primarily from 1) the topology of the collagen-elastin network and 2) the mechanical interaction between proteoglycans and fibers. We measured the quasi-static, uniaxial stress-strain curves of lung tissue sheets in hypotonic, normal, and hypertonic solutions. We found that the stress-strain curve was sensitive to osmolarity, but this sensitivity decreased after proteoglycan digestion. Images of immunofluorescently labeled collagen networks showed that the fibers follow the alveolar walls that form a hexagonal-like structure. Despite the large heterogeneity, the aspect ratio of the hexagons at 30% uniaxial strain increased linearly with osmolarity. We developed a two-dimensional hexagonal network model of the alveolar structure incorporating the mechanical properties of the collagen-elastin fibers and their interaction with proteoglycans. The model accounted for the stress-strain curves observed under all experimental conditions. The model also predicted how aspect ratio changed with osmolarity and strain, which allowed us to estimate the Young's modulus of a single alveolar wall and a collagen fiber. We therefore identify a novel and important role for the proteoglycans: they stabilize the collagen-elastin network of connective tissues and contribute to lung elasticity and alveolar stability at low to medium lung volumes.

No abstract

The mean linear intercept (L(m)) can be used to estimate the surface area for gas exchange in the lung. However, in recent years, it is most commonly used as an index for characterizing the enlargement of airspaces in emphysema and the associated severity of structural destruction in the lung. Specifically, an increase in L(m) is thought to result from an increase in airspace sizes. In this paper, we examined how accurately L(m) measures the linear dimensions of airspaces from histological sections and a variety of computer-generated test images. To this end, we developed an automated method for measuring linear intercepts from digitized images of tissue sections and calculate L(m) as their mean. We examined how the shape of airspaces and the variability of their sizes influence L(m) as well as the distribution of linear intercepts. We found that, for a relatively homogeneous enlargement of airspaces, L(m) was a reliable index for detecting emphysema. However, in the presence of spatial heterogeneities with a large variability of airspace sizes, L(m) did not significantly increase and sometimes even decreased compared with its value in normal tissue. We also developed an automated method for measuring the area and computed an equivalent diameter of each individual airspace that is independent of shape. Finally, we introduced new indexes based on the moments of diameter that we found to be more reliable than L(m) to characterize airspace enlargement in the presence of heterogeneities.

Cell mechanical properties on a whole cell basis have been widely studied, whereas local intracellular variations have been less well characterized and are poorly understood. To fill this gap, here we provide detailed intracellular maps of regional cytoskeleton (CSK) stiffness, loss tangent, and rate of structural rearrangements, as well as their relationships to the underlying regional F-actin density and the local cytoskeletal prestress. In the human airway smooth muscle cell, we used micropatterning to minimize geometric variation. We measured the local cell stiffness and loss tangent with optical magnetic twisting cytometry and the local rate of CSK remodeling with spontaneous displacements of a CSK-bound bead. We also measured traction distributions with traction microscopy and cell geometry with atomic force microscopy. On the basis of these experimental observations, we used finite element methods to map for the first time the regional distribution of intracellular prestress. Compared with the cell center or edges, cell corners were systematically stiffer and more fluidlike and supported higher traction forces, and at the same time had slower remodeling dynamics. Local remodeling dynamics had a close inverse relationship with local cell stiffness. The principal finding, however, is that systematic regional variations of CSK stiffness correlated only poorly with regional F-actin density but strongly and linearly with the regional prestress. Taken together, these findings in the intact cell comprise the most comprehensive characterization to date of regional variations of cytoskeletal mechanical properties and their determinants.

. Lung and alveolar wall elastic and hysteretic behavior in rats: effects of in vivo elastase treatment. J Appl Physiol 95: 1926-1936, 2003. First published July 18, 2003 10.1152/japplphysiol.00102. 2003.-We investigated the relationship between the microscopic elastic and hysteretic behavior of the alveolar walls and the macroscopic mechanical properties of the whole lung in an in vivo elastase-treated rat model of emphysema. We measured the input impedance of isolated lungs at three levels of transpulmonary pressure (Ptp) and used a linear model to estimate the dynamic elastance and hysteresivity of the lungs. The elastance of the normal lungs increased steeply with Ptp, whereas this dependence diminished in the treated lungs. Hysteresivity decreased significantly with Ptp in the normal lungs, but this dependence disappeared in the treated lungs. To investigate the microscopic origins of these changes, the alveolar walls were immunofluorescently labeled in small tissue strips. By using a fluorescent microscope, the lengths and angular orientations of individual alveolar walls were followed during cyclic uniaxial stretching of the tissue strips. The microstrains (relative change in segment length) and changes in angle of the alveolar walls showed considerable heterogeneity, which was interpreted in terms of a network model. In the normal strips, the alveolar walls showed larger angular changes compared with the treated tissue, whereas the alveolar walls of the treated tissue tended to be more extensible. Hysteresis in the average angle change was also larger in the treated tissue than in the normal tissue. We conclude that the decreased Ptp dependence of elastance and the constant hysteresivity in the treated lungs are related to microstructural remodeling and network phenomena at the level of the alveolar walls.

Capillarity is the study of interfaces between two immiscible liquids or between a liquid and a vapor. The theory of capillarity was created in the early 1800s, and it is applicable to mesoscopic and macroscopic (>1 μm) systems. In general, macroscopic theories are expected to fail at the <10 nm scales where molecular details may become relevant. In this work, we show that, surprisingly, capillarity theory (CT) provides satisfactory predictions at 2−10 nm scales. Specifically, we perform atomistic molecular dynamics (MD) simulations of water droplets and capillary bridges of different symmetry in contact with various surfaces. The underlying structure of the surfaces corresponds to hydroxilated (crystalline) silica which is modified to cover a wide range of hydrophobicity/hydrophilicity. In agreement with CT, it is found that water contact angle is independent of the droplet/bridge geometry and depends only on the hydrophobicity/hydrophilicity of the surface employed. In addition, CT provides the correct droplet/bridge profile for all (hydrophobic/hydrophilic) surfaces considered. Remarkably, CT works even for the very small droplets/bridges studied, for which the smallest dimension is ≈2 nm. It follows that the concepts of surface tension and contact angle are indeed meaningful at 2−10 nm scales even when, macroscopically, such concepts are not justified. In order to confirm the self-consistency of CT at 2−10 nm scales, we also calculate the capillary forces between different surfaces induced by water capillary bridges. These forces depend on the liquid−vapor surface tension of water, γ. Using CT, the calculated forces indicate that γ = 0.054 ± 0.001 N/m 2 . This is in agreement with the value γ = 0.056 ± 0.001 N/m 2 obtained independently using the Kirkwood−Buff method, and it is consistent with values of γ reported in the literature for the present water model. Confirming the validity of CT at 2−10 nm scales has relevant implications in scientific applications, such as in our understanding of selfassembly processes at interfaces. We discuss briefly this and other consequences of the present results.

We study the distribution Pi(n)(D) of airway diameters D as a function of generation N in asymmetric airway trees of mammalian lungs. We find that the airway bifurcations are self-similar in four species studied. Specifically, the ratios of diameters of the major and minor daughters to their parent are constants independent of N until a cutoff diameter is reached. We derive closed form expressions for Pi(N)(D) and examine the flow resistance of the tree based on an asymmetric flow division model. Our findings suggest that the observed diameter heterogeneity is consistent with an underlying regular branching asymmetry.